Lecture Notes ASTR 1000 Fall 2009 Slide Set #1 Celestial Motions Dr. H.A. McAlister Dept. of Physics & Astronomy Geo

1. Lecture Notes ASTR 1000 Fall 2009 Slide Set #1 Celestial Motions Dr. H.A. McAlister Dept. of Physics & Astronomy Georgia State University

2. The Constellations • 88 constellations in the sky. Those in the northern celestial hemisphere named by the Greeks. Constellations in the extreme southern sky were named in modern times. • Subsets of constellations are called asterisms. For example, the “Big Dipper” is an asterism of the constellation Ursa Major (the big bear). • While constellations were named by the Greeks, Arabic names have been mostly adopted for individual stars. Stars within a constellation are assigned Greek letters in accordance with their brightest. For example, the brightest star in Orion has the Arabic name Betelgeuse, but it is also known as a Orionis. Orion’s second brightest star, Rigel, is also called b Orionis. • The twelve constellations lying along the projection of the Earth’s orbit onto the sky (the ecliptic) comprise the zodiac.

3. Winter Sky – Facing North

4. Winter Sky – Facing South

5. Orion as Depicted by J. Hevelius (1690) (Note that this is as viewed from outside celestial sphere)

6. Spring Sky – Facing North

7. Spring Sky – Facing South

8. Celestial Motions • The rotation of the Earth about its spin axis once every 24 hours causes diurnal effects including day and night and the rising and setting of celestial objects. • The revolution of the Earth about the sun once every 365.2422… days produces annualeffectssuch as the sun appearing to move with respect to the stars along a path in the sky called the ecliptic. The twelve constellations lying along the ecliptic comprise the zodiac. • The apparent motions of celestial objects on the sky are the combined result of diurnal and annual motions and, in the case of the planets their own orbital motions around the sun.

9. The Celestial Sphere north celestial pole Earth’s spin axis north pole equator celestial equator south pole celestial sphere south celestial pole

10. Terrestrial Coordinates N * Greenwich * Atlanta latitude Equator longitude S For Atlanta: latitude = 33o 45’ N longitude = 84o 23’ W

11. Lunar Months All motions are counterclockwise Time from t1 to t2 is the “sidereal month” (This is time required for realignment with respect to the stars and equals 27.3 days.) t1 Time from t1 to t3 is the “synodic month” (This is the time between repetition of phases and equals about 29.5 days. This is what we use for our calendar.) t2 t3

12. Lunar Phases first quarter waxing gibbous waxing crescent sunlight sunset full moon new moon noon midnight to the Sun sunrise Earth waning gibbous waning crescent sunlight third quarter

13. Questions About Lunar Phases • What is the time interval between new and full moons? • What time does the full moon culminate? • What time does the new moon culminate? • What time does the new moon rise? • What is the phase of the moon that culminates at sunset? • What is the phase of the rising moon at sunset? • What is the phase of the setting moon at midnight? two weeks midnight noon sunrise first quarter full first quarter

14. “Earthshine” waxing crescent Moon Sunlight reflected off day lit side of Earth illuminates dark part of crescent moon. sunlight to the Sun Earth The effect is most obvious just before and just after new moon sunlight

15. The Tides 4. On the far side, the Earth is effectively pulled Moonward away from the water, yielding another high tide. 3. The water on the near side of the Moon is pulled away from Earth, raising a high tide. Earth Moon 2. The presence of the Moon produces a gravitational attraction on the Earth whose strength varies inversely with distance from the Moon. 1. Imagine a perfectly spherical Earth uniformly flooded by an ocean.

16. Moon Factoids • A “blue moon” is when more than one full moon occurs in the same calendar month. • The moon undergoes “synchronous” rotation and revolution (i.e. the periods of rotation and revolution are identical), so one side of the moon always faces the Earth. • The “harvest moon” involves the rising of the full moon in late September and early October. Due to the angular tilt of the moon’s orbital plane with that of the Earth, the bright moon appears to rise at about the same time in the early evening when the moon is full at the time of the “autumnal equinox”.

17. Moon Myths • The phase of the moon has no effect on human behavior. • There is no such thing as the “dark side of the moon.” • We did indeed land humans on the moon in the six Apollo landings between July 1969 and December 1972. • For more about “lunatics”, the “moon hoax” and other astronomical pseudoscience, see: • www.astrosociety.org/education/resources/pseudobib.html

18. Tilt of Earth’s Spin Axis 23.5o tilt The Earth’s spin axis is tilted by 23.5 degrees off vertical with respect to the “ecliptic plane” (plane of the Earth’s orbit around the sun) The spin axis remains essentially parallel to itself during the course of the year

19. Summer Solstice – 21 June tropic of Cancer arctic circle sunlight equator antarctic circle sunlight

20. Winter Solstice – 21 December tropic of Cancer arctic circle sunlight equator antarctic circle sunlight tropic of Capricorn

21. Vernal Equinox – 21 March arctic circle sunlight tropic of Cancer equator tropic of Capricorn sunlight antarctic circle

22. Autumnal Equinox – 21 September arctic circle sunlight tropic of Cancer equator tropic of Capricorn sunlight antarctic circle

23. The Culminating Sun • The sun culminates in the zenith (i.e. straight overhead) at noon for observers located on the tropic of Cancer (latitude = 23.5o N) on the day of the summer solstice. • The sun culminates in the zenith at noon for observers located on the tropic of Capricorn (latitude = 23.5o S) on the day of the winter solstice. • The sun culminates in the zenith (i.e. straight overhead) at noon for observers located on the equator (latitude = 0o) on the days of the equinoxes.

24. Other Seasonal Extremes • The sun never rises for observers north of the arctic circle on the day of the winter solstice • The sun never sets for observers north of the arctic circle on the day of the summer solstice • The above conditions are reversed for the antarctic circle. • The sun moves 360o around the horizon for observers located at the north and south poles on the days of the equinoxes.

25. Tilt of Earth’s Spin Axis W N S E winter solstice summer solstice equinox The sun rises on the east point and sets on the west point on the days of the equinoxes, giving equal periods of “day” and “night”. The sun is in the sky for the longest duration on the summer solstice and illuminates the northern hemisphere most directly.

26. Temperature Effect • Summer days are longer and the sun is more intense (due to the more direct illumination angle). Thus summer is hotter than winter. • There is a lag of the seasons when comparing the dates of the solstices with the actual extremes in temperature because it takes time to heat up the oceans and atmosphere at the onset of summer and to cool them off at the onset of winter. • If the Earth’s spin axis were not tilted by some angle, we would have no seasons.

27. Precession of Earth’s Spin Axis 5. Spin axis now points to Polaris. 13,000 years from now, Vega will be our “pole star” 4. Earth responds to this pull by slowly “precessing” its spin axis around a circle in the sky once every 26,000 years 23.5o 2. Moon’s orbital plane is tilted by 5o from our equator 3. Moon’s gravitational pull on Earth attempts to pull bulge into lunar orbital plane 1. The rotation of the Earth distorts it into an “oblate” spheroid flattened at the poles

28. Shadows and Eclipses Sun Penumbra Umbra Earth

29. Eclipse of the Moon (Lunar Eclipse) Earth’s Orbit Moon’s Orbit Occurs at Full Phase when Moon is also at the “line of nodes” of its orbit with respect to the ecliptic A lunar eclipse lasts for many hours and can be seen from the majority of the Earth’s surface

30. Eclipse of the Sun (Solar Eclipse) Earth’s Orbit Moon’s Orbit Occurs at New Phase when Moon is also at the “line of nodes” of its orbit with respect to the ecliptic A solar eclipse lasts for only for a few minutes and can only be seen from very restricted locations on the Earth’s surface

31. Total and Annular Eclipses Vertex of Umbral shadow is at or below Earth’s surface, so a total eclipse is possible Vertex of Umbral shadow is above Earth’s surface, so only an annular eclipse is possible

32. Example of a Solar Eclipse Path See Richard Monk’s webpage on eclipses: www.williams.edu/ astronomy/IAU_eclipses/

33. Total Solar Eclipse of 21 June 2001 from Zimbabwe See Richard Monk’s webpage on eclipses: www.williams.edu/ astronomy/IAU_eclipses/ Bailey’s Beads Solar Corona “Diamond Ring”

34. Upcoming Lunar and Solar Eclipses Solar Eclipses: 15 Jan 2009 (annular) – Asia & Africa 11 July 2010 (total) – South Pacific Ocean 4 Jan 2011 (partial) – Europe, Africa & central Asia 1 Jun 2011 (partial) – east Asia, far N. America, Iceland 1 Jul 2011 (partial) – south Indian Ocean 25 Nov 2011 (annular) – south Africa, Antactica, Tasmania, New Zealand The next total solar eclipses visible from the U.S. will be on 21 Aug 2017 and 8 Apr 2024. The 2017 eclipse will be visible from Georgia. Lunar Eclipses: 31 Dec 2009 – not U.S. 15 Jan 2010 (annular) – not U.S. 26 Jun 2010 (partial) – not U.S. 21 Dec 2010 (total) – all U.S. 15 Jun 2011 (total) – not U.S. 10 Dec 2011 (total) – all U.S.

35. Motions of the “Wanderers” – The Planets retrograde motion normal “direct” (eastward) motion Mars East West The night sky facing south

36. The Geocentric Explanation All motions are circular direct Epicycle moves at constant angular rate about the equant epicycle Mars retrograde Adjustable parameters include diameters of epicycle & deferent, distance of equant from deferent center, and rates of motion along epicycle & deferent stationary Earth . + equant deferent center deferent Developed in detail around 140 AD by Claudius Ptolemy and very successfully used for 1500 years!

37. The Heleocentric Explanation direct motion retrograde motion around “opposition” Sun direct motion Earth Mars First proposed in detail by Nicolaus Copernicus in ~1505 but not published until De Revolutionibus in 1543.

38. Oppositions of Mars “Favorable” Opposition Earth is at aphelion closest approach is 34 million miles Mars is at perihelion “Unfavorable” Opposition Earth is at perihelion closest approach is 68 million miles Mars is at aphelion Oppositions of Mars occur at 26-month intervals On 27 Aug 2003, Mars had its most favorable opposition in 73,000 years

39. Orbital Configurations for an Inferior Planet Maximum Eastern Elongation Inferior Conjunction Superior Conjunction Earth Sun Maximum Western Elongation

40. Orbital Configurations for a Superior Planet Eastern Quadrature Opposition Earth Conjunction Sun Western Quadrature

41. Giants of the Heliocentric Theory • Nicolaus Copernicus (1473-1543) – Developed the Heliocentric Theory but waited until just before his death to release his great book, De Revolutionibus. • Tycho Brahe (1546-1601) – Greatest pre-telescopic observer, produced extensive observations of Mars that were critical to proving the Heliocentric Theory. • Johannes Kepler (1571-1630) – Hired as Tycho’s assistant but only gained access to Tycho’s complete data after Tycho’s premature death. Kepler discovered three “laws of planetary motion” that revolutionized the understanding of the solar system. • Galileo Galilei (1564-1642) – First used the telescope for observing the night sky in 1609. His discoveries were monumental and included proof of the Heliocentric Theory. • Isaac Newton (1642-1727) – Developed the Law of Universal Gravitation and three laws of motion that completely explain Kepler’s Laws of Planetary Motion.

42. Kepler’s First Law Planets revolve around the sun in elliptical orbits with the sun located at one focus of the ellipse planet sun + center focus focus

43. Kepler’s Second Law The line from the sun to a planet sweeps out equal areas in equal time intervals. t1 areaA t2 t4 aphelion (slowest) perihelion (fastest) areaB areaA = areaB if t2-t1 = t4-t3 t3

44. Kepler’s Third Law For any two planets, the ratio of their mean distance from the sun cubed equals the ratio of their orbital periods squared. (D1/D2)3 = (P1/P2)2 Planets far from the sun take longer to orbit the sun than do planets nearer the sun.

45. Galileo’s Telescopic Discoveries • New Stars – Discovered that his telescopes revealed far more stars than are accessible to the unaided eye. • Lunar Feature – Found the moon to have craters, mountains and complicated terrain. He also reported spots on the sun, although it turns out they had first been reported centuries earlier by Chinese astronomers. • Rings of Saturn – Galileo reported that Saturn had “ears” as his telescopes couldn’t quite make out the true nature of the rings. • Satellites of Jupiter – Discovered four large moons of Jupiter (still often referred as the “Galilean satellites”) which clearly orbited Jupiter and contradicted the geocentric premise that all bodies move around the Earth. • Phases of Venus – He discovered that Venus exhibited a complete cycle of phases, which it could not do under the constraints of the geocentric theory. This was proof of the heliocentric theory.